Mathematical boat design method

[Wayne Grabow]

I am a total amateur at boat design/building but have been using a mathematical technique to create developable hull shapes which I have not seen mentioned elsewhere, so I've done a descriptive overview with a sample hull shape. I know that it works because I have already built six boats using this technique. What I am wondering is if I "discovered" something that many others are already using, or might this be something new and possibly useful?

What I like is the absolute dimensional accuracy and resulting fairness of the hull shape. Dimensions are calculated before the surfaces are drawn. Working with developable surfaces should facilitate the building process also.

http://developable-surface-boat-designs.blogspot.com/

[amolitor]

I don't really see what's new about it, although I confess I did just skim. It does look like you've assembled a useful "toolkit" of techniques, and applied them pretty well.

I didn't see anywhere where you discussed "flattening" your surfaces out? Do you have a good way to do that, or do you just cut-and-try?

[Wayne Grabow]

My impression is that, traditionally, boats are designed by making scaled drawings, taking offsets from the drawings, and then scaling the offsets up to full size. When actual construction is contemplated, the design must be lofted to check for and correct scaling/drafting errors. With modern computer-based programs that may not be so. If so, then you are right that there may be nothing new here. I'd like to find out.

Because I am working in abstract space, the hull shape is designed full size and the offsets are initially calculated as full size dimensions which can be accurate to as many significant figures as you care to use. Scaling is only used to reduce the design so that it will fit on paper for viewing. Because the technique is fully based on developable surface concepts, it can be guaranteed that the surfaces can be sheathed with sheet materials without distortion.

When I initially started using this approach, I "flattened" all surfaces so that panels could be simply cut out and put in place. But, at that time, I restricted myself to simpler shapes. Now that I'm using a less restrictive "toolkit" of techniques, I no longer try to flatten the surfaces for fabrication. It could be done but, for me, is not worth the effort. Instead I use thin (cheap) plywood to make a pattern. The principal drawbacks of this approach are that it is restricted to developable shapes only (using multiple chines can help offset that), and it requires a full skeleton of frames or molds to establish the shape.

Thank you for your comments.

[Guest625101138]

Originally Posted by Wayne Grabow

My impression is that, traditionally, boats are designed by making scaled drawings, taking offsets from the drawings, and then scaling the offsets up to full size. When actual construction is contemplated, the design must be lofted to check for and correct scaling/drafting errors. With modern computer-based programs that may not be so. If so, then you are right that there may be nothing new here. I'd like to find out.

Because I am working in abstract space, the hull shape is designed full size and the offsets are initially calculated as full size dimensions which can be accurate to as many significant figures as you care to use. Scaling is only used to reduce the design so that it will fit on paper for viewing. Because the technique is fully based on developable surface concepts, it can be guaranteed that the surfaces can be sheathed with sheet materials without distortion.

When I initially started using this approach, I "flattened" all surfaces so that panels could be simply cut out and put in place. But, at that time, I restricted myself to simpler shapes. Now that I'm using a less restrictive "toolkit" of techniques, I no longer try to flatten the surfaces for fabrication. It could be done but, for me, is not worth the effort. Instead I use thin (cheap) plywood to make a pattern. The principal drawbacks of this approach are that it is restricted to developable shapes only (using multiple chines can help offset that), and it requires a full skeleton of frames or molds to establish the shape.

Thank you for your comments.

The majority of low production runs are just laser cut from CAD files for developable construction. If it is not developable then a full size foam plug will be milled as the basis for producing a mould. Drawings are less commonly used these days even for amateur builds.

There are algorithms available such as Michlet/Godzilla that will generate an optimum hull for set constraints and these are used as the starting point for hull design.

Rick W

[Wayne Grabow]

I had a batch of steel plates laser cut to join the exposed beams in our home, but those were easy shapes requiring only simple drawings. To produce the CAD files for a complex developable hull shape would likely require use of a compatible commercial computer-based design program. Way beyond where I am at, but it's nice to know what is state of the art.

[Tad]

Wayne...

I'm no mathematician, but I believe what you have "discovered" was first implemented by Dr. John Letcher in the late 1970's when cheap programmable calculators first became available. Mathematical line fairing on a calculator lead to use with the very first PC's, and creation of the Fairline program. John Letcher's company is now known as AeroHydro.

[Earl Boebert]

As far as I know, the best work on the geometric method of developed hull surfaces is by S.S. Rabl entitled "Multiconic Design of Hull Surfaces." I have used the process and it works, but is tedious. It appeared in "The Planimeter," Journal of the Society of Small Craft Designers, March 1958, was also reprinted by Kaiser Aluminum, and I reprinted it in "The Model Yacht," newsletter of the U.S. Vintage Model Yacht Group, Volume 9 No 3. PM me with an email if you'd like a PDF copy.

I believe this method, or something like it, is used in the Hulls program of Carlson Hull Design (www.carlsondesign.com) which has been used for years and has an extensive library of designs associated with it. I first design my chined hulls using Delftship to get an "almost developable" hull, then move the dimensions over to the Carlson program to get the surface shapes. It works well, but has a user interface that will encourage you to practice your salty language :-)

Cheers,

Earl

[Ike]

Tad's right. I've known John Letcher since the mid eightes when I took his class on CAD design. He came from the aircraft industry and was a mathematician. He developed a way to calculate b spline curves using a hand calculator, and then (believe it or not) a program for the Radio Shack TRS 80 (commonly called a TRASH 80) with 4 KB of ram. The amazing thing is, it worked. Using a set of coordinates you could develope curves and then a set of curves that defined the shape of the boat. Eventually he went on to PCs and much more powerful stuff. However, the early stuff was not developable surfaces, and chines played hell with the program. But there were work-arounds so you could draw lines drawings with chines. It just took a little more effort.

[Guest625101138]

Originally Posted by Wayne Grabow

I had a batch of steel plates laser cut to join the exposed beams in our home, but those were easy shapes requiring only simple drawings. To produce the CAD files for a complex developable hull shape would likely require use of a compatible commercial computer-based design program. Way beyond where I am at, but it's nice to know what is state of the art.

Wayne
The programs are not expensive. Michlet/Godzilla which generates optimum slender hulls is free as is Delftship (Freeship in earlier guise). The latter has the ability to produce cutting files for developable plates. It is a little tedious to learn but once you grasp it the results are good.

There are other free software packages that do the same thing but the ones mentioned are probably in most common use here.

I make all my bits by hand so I go through some sort of lofting process from various tables I produce in Delftship but I have had a copy of one of my boats milled from foam that was used as male plug. The 3D file was taken straight from Delftship. I have had a propeller milled from aluminium that was also drawn in Delftship. So the program is quite flexible in what you can do with it.

Rick W

[Wayne Grabow]

Thank you all for getting me out of my time capsule and up to date. I did a college engineering research project (early 70's) on hull design. We, of course, worked with the big IBM computers, and I had this idea that if one could mathematically describe a hull shape and use the power of electronic computation, hull design could really progress. But the job market for a young engineer in the early 70's was limited, so I completely changed careers and became engrossed in a new field of endeavor.

Since then I occasionally had time to design and quickly build something simple using my original concepts, but nothing more. It was my only connection to my original engineering training. Recently, on another website, I read entries of people manually drafting designs and complaints of inaccurate offsets on plans, so I wasn't sure much progress had been made.

I appreciate all the enlightening comments.

[InetRoadkill]

I did my hull using a 3d rendering program that has good NURBS surface support. It's nice and fair. The trick is that you need to be careful with NURBS since you can introduce ripples. The big question is how efficient is it. I would love to optimize it on a CFD program, but that's a bit pricey.

[Gilbert]

Well, Wayne, even though the other software mentioned will produce good results, I do have the impression that your technique is rather unique. What most builders want to know is "Is it a developable surface? And if it is, can you give me accurate sections for a form or accurate dimensions of the panels?" From what you are saying, I gather that your method focuses very directly on accurate sections for use as frames or a building form without a lot of tedious trial and error, but perhaps a little trial and error. That sounds pretty useful to me.
I use software routines based on Ulman Kilgore's mathematical formulas for finding ruling lines between two three dimensional curves. Your mathematical abilities might give you a leg up on understanding his method. You could find out more by doing a search on this forum.

[Tcubed]

I would have liked it more if there were more detail in your blog.

From what i can tell your method will guarantee a developable surface and will give you an infinite set of different surfaces but this is a subset of all possible developable surfaces .

Just like aleph 1 , aleph 2 etc ( the different levels of infinity like for example there is an infinite set of rational numbers which is a subset of all the real numbers)

The method from what i can gather from your blogpost is actually one i had already thought of but never put into practice.

[Wayne Grabow]

"What most builders want to know is "Is it a developable surface? And if it is, can you give me accurate sections for a form or accurate dimensions of the panels?" From what you are saying, I gather that your method focuses very directly on accurate sections for use as frames or a building form without a lot of tedious trial and error, but perhaps a little trial and error. That sounds pretty useful to me."

Gilbert, you are right. Any desired cross section can be calculated by setting X equal to the desired quantity and projecting all coordinates which pass through that plane. Similarly, horizontal cross sections (waterlines) could be calculated by choosing a value for Z and doing similar projections; and likewise for Y values. This is all possible because the subject is developable surfaces; by definition there are many ruling lines in these surfaces. I don't have to "find" these ruling lines; I create a set of them. From the chine description alone (in this example) I can easily provide exact coordinates every 3.5" which provides more than enough data to closely describe these sections. Just connect the (closely-spaced) dots. I don't want to restate my initial description, but the concepts are simple: 1-a mathematical chine description, 2-projections in space, either point-slope or between two points. The more interesting part is deciding which type of projection to use (planar, parallel,or conic), positioning the apex or slope, and then linking multiple projections along common ruling lines to create more complex shapes.

"I would have liked it more if there were more detail in your blog."

Tcubed, you are the first person to ever say that. I am always afraid that people get lost in the details, their eyes glaze over, and they zone out. I'd be happy to describe a specific issue; otherwise, I won't know when to stop and may waste your time.

[Earl Boebert]

Originally Posted by Wayne Grabow

[Tcubed said] "I would have liked it more if there were more detail in your blog."

Tcubed, you are the first person to ever say that. I am always afraid that people get lost in the details, their eyes glaze over, and they zone out. I'd be happy to describe a specific issue; otherwise, I won't know when to stop and may waste your time.

A useful approach, if your blog rules permit, is to have a PDF attachment containing the blood and gore :-) I too would be interested in reading more.

Cheers,

Earl